devtools::install_github("gledguri/QM",dependencies = TRUE, force = T )
library(QM)
load_QM_packages()Quantitative Metabarcoding
0.1 Load the package and its dependencies
0.2 Load the data
data(qpcr);force(qpcr)
data(metabarcoding);force(metabarcoding)qpcr# A tibble: 817 × 7
Well Sample_name Species Sample_type Ct Plate Std_concentration
<chr> <chr> <chr> <chr> <chr> <chr> <dbl>
1 A1 Std-CS1 Gadus morhua STANDARD 17.17366409 Plate_A 1000000
2 B1 Std-CS2 Gadus morhua STANDARD 20.32516289 Plate_A 100000
3 C1 Std-CS3 Gadus morhua STANDARD 24.26965332 Plate_A 10000
4 D1 Std-CS4 Gadus morhua STANDARD 26.89413261 Plate_A 1000
5 E1 Std-CS5 Gadus morhua STANDARD 30.73742294 Plate_A 100
6 F1 Std-CS6 Gadus morhua STANDARD 33.8976326 Plate_A 10
7 G1 Std-CS7 Gadus morhua STANDARD 36.95103073 Plate_A 1
8 A2 Std-CS1 Gadus morhua STANDARD 17.41136169 Plate_A 1000000
9 C2 Std-CS3 Gadus morhua STANDARD 24.2088623 Plate_A 10000
10 D2 Std-CS4 Gadus morhua STANDARD 27.22113228 Plate_A 1000
# ℹ 807 more rowsmetabarcoding# A tibble: 10 × 93
Species sp_idx ini_conc Mock_1 Mock_2 Mock_3 Mock_4 Mock_5 Mock_6 `2019629_11` `2019629_15` `2019629_16` `2019629_22` `2019629_28` `2019629_31` `2019629_32` `2019629_6` `2019629_7` `2020620_03` `2020620_04` `2020620_05` `2020620_06` `2020620_07` `2020620_08` `2020620_11` `2020620_12` `2020620_13` `2020620_14` `2020620_15` `2020620_16` `2020620_19` `2020620_20` `2020620_21` `2020620_22` `2020620_23` `2020620_24` `2020620_27` `2020620_28` `2020620_29` `2020620_30` `2020620_31` `2020620_32` `2021624_10` `2021624_11` `2021624_14` `2021624_15` `2021624_16` `2021624_17` `2021624_18` `2021624_19` `2021624_20` `2021624_21` `2021624_22` `2021624_25` `2021624_26` `2021624_27` `2021624_28` `2021624_29` `2021624_3` `2021624_30` `2021624_31` `2021624_32` `2021624_33` `2021624_36` `2021624_37` `2021624_38` `2021624_39` `2021624_4` `2021624_40` `2021624_41` `2021624_42` `2021624_43` `2021624_44` `2021624_5` `2021624_6` `2021624_7` `2021624_8` `2021624_9` `2019629_12` `2019629_13` `2019629_14` `2019629_19` `2019629_20` `2019629_21` `2019629_23` `2019629_24` `2019629_27` `2019629_29` `2019629_3` `2019629_30` `2019629_4` `2019629_5` `2019629_8`
<chr> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int>
1 Brosme brosme 1 6022 26537 26282 55800 37606 34698 82587 0 0 0 0 0 2 0 0 6 2 1782 0 2 0 0 0 2 0 2 0 0 2 0 0 2 0 0 0 0 0 2 0 0 0 0 10 2 0 6 0 0 2 0 0 2 0 2 2 4 0 10 0 4 0 2 0 0 0 0 0 0 6 0 0 0 0 0 2 2 0 0 1 0 0 0 7 2 0 0 2 0 0 1 0
2 Cyclopterus lumpus 2 12061 63611 38494 80634 58797 37921 95245 2 0 0 2 0 0 0 0 0 4 2 0 2 4 0 0 0 6 0 8 0 0 0 0 4 0 0 0 0 2 4 0 0 2 4 0 0 0 2 0 0 0 2 0 12 4 0 10 0 4 22 4 30 2 2 10 2 6444 0 2 0 1114 0 0 0 0 2 8 2 0 3 6 1 3 0 12 1 1 1 18 90138 2 0 4
3 Hippoglossoides platessoides 3 6812 103953 53527 96043 83638 50442 118507 8214 0 0 6890 2 0 2 13672 4 17624 20868 0 5686 10148 6574 350 0 6 22342 4 7552 24912 0 12842 17432 4 10 9522 34610 10024 27240 22970 10798 28 6 16172 0 0 8272 8308 8 13990 8 4340 244510 360158 113176 477728 233486 25768 510300 240732 543826 63728 85020 3722 20754 40130 3822 4332 15434 99374 30014 23738 0 1580 1512 5490 13680 1 10716 67511 20325 1203 1 13598 2 7871 18 21045 14509 9 6 3
4 Leptoclinus maculatus 4 3725 228228 124488 237519 194652 107854 256737 160 0 0 6800 0 0 0 5240 0 4 848 0 3274 746 0 0 0 0 0 2 0 0 0 0 254 0 0 0 0 0 3020 5034 0 2 2 2 0 0 0 0 0 0 2 0 1336 0 0 5584 2 2046 0 66 1024 0 2312 18044 2 1430 0 582 0 724 0 0 0 294 3372 2 0 1 5 21640 5 4 2 218 2 1 2 2016 22234 5348 4 0
5 Mallotus villosus 5 9816 72751 35851 94465 58157 31141 90112 70304 3100 6 4 10 0 10 1372 6580 242 2040 4 256 0 0 210 5816 436 15670 10472 2 780 4 4 26074 4454 15910 1640 7958 3552 20624 6072 2 3432 4750 26782 1502 496 4 2 14 4004 14 4 48540 10376 239346 39828 12914 12 9548 15520 98442 16534 6886 3704 6 2534 12 4 10 12658 8 6 4 7354 5094 74 3270 5 11 13 3 10 0 11 73 2 6 9830 3047 40385 860 226
6 Maurolicus muelleri 6 7087 99815 29082 130790 120742 58762 162580 0 0 0 0 2 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 0 4 0 0 0 0 1 3 0 0 3 0 0 0 1 0 0 3 1
7 Myoxocephalus scorpius 7 8908 75120 44139 77521 70449 48500 91900 0 0 0 2 0 0 0 0 0 6 4 0 0 2 10 0 2 2 0 2 0 2 0 0 4 0 0 2 0 0 0 2 2 2 0 4 0 2 0 0 0 2 0 0 4 2 0 2 6 2 14 4 10 0 0 2 0 4 2 2 0 18 0 0 0 0 0 2 0 0 1 2 0 0 0 2 0 0 1 6 3 2 0 0
8 Pholis gunnellus 8 4477 66110 36235 58501 52223 38270 75811 100 694 0 2936 2 834 0 9916 0 2446 3070 4 3306 5562 1146 0 0 2218 4 5542 3176 0 0 4 556 0 0 2428 0 9314 1448 2034 4 824 6954 14 2866 0 1702 0 2 0 2 0 1194 14 6 3068 574 2410 16 1388 2508 4 1094 8266 5300 4572 0 734 0 2678 0 0 2 830 1420 7630 1884 0 0 1 0 0 0 0 0 0 1 12 3 1 0 0
9 Pleuronectes platessa 9 2637 41550 19983 44716 44234 27283 63749 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 Zz_Gadus morhua 10 5942 72763 56460 111345 82212 52685 112193 8514 8 1752 4462 5630 4822 26164 78346 50714 50744 17520 2622 32848 44932 2036 272 22108 0 25250 2 0 25320 16498 1482 12430 20104 7386 3100 12350 0 14652 11836 4 22106 5912 70490 4274 8420 17494 8180 8 25790 12904 14 30104 23940 13508 65144 11634 17790 88546 15530 49048 6 32758 694 186 18264 8326 18766 4664 79992 4 5492 1652 17274 8860 4160 48536 3 6 23677 0 5 0 11638 4592 7772 36686 18466 20476 29841 8 20.3 Run Model 1
Here we make use of the standard concentration to learn the parameters that link the known DNA concentration with observed Ct values (Y) and positive / negative qPCR amplification (Z)
\[ \begin{aligned} &\textbf{qPCR probability of detection model}\\ Z_{ij} &\sim \text{Bernoulli}(\theta_{i}) && \text{(1.1)} \\ \theta_{i} &= 1 - exp(-W_{i} \cdot \phi) && \text{(1.2)} \\ &\text{}\\ &\textbf{qPCR continuous model}\\ Y_{ij} &\sim \text{Normal}(\mu_{i}, \sigma_{i}) && \text{(2.1)} \\ \mu_{i} &= \beta0_{p} + \beta1 \cdot ln(C_{i}) && \text{(2.2)} \\ \sigma_{i} &= e^{(\gamma0 + \gamma1 \cdot ln(C_{i}))} && \text{(2.3)} \end{aligned} \]
M1 <- load_model('M1')Trying to compile a simple C fileRunning /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
using C compiler: ‘Apple clang version 16.0.0 (clang-1600.0.26.6)’
using SDK: ‘MacOSX15.2.sdk’
clang -arch arm64 -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DUSE_STANC3 -DSTRICT_R_HEADERS -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION -D_HAS_AUTO_PTR_ETC=0 -include '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/opt/R/arm64/include -fPIC -falign-functions=64 -Wall -g -O2 -c foo.c -o foo.o
In file included from <built-in>:1:
In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp:22:
In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/Dense:1:
In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/Core:19:
/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:679:10: fatal error: 'cmath' file not found
679 | #include <cmath>
| ^~~~~~~
1 error generated.
make: *** [foo.o] Error 1# Prepare the data for going into the model
stan_data_M1 <- prep_stan_M1(
qpcr_data = qpcr %>% filter(Sample_type=="STANDARD"),
Ct = "Ct",
standard_concentration = "Std_concentration",
plate_index = 'Plate')Plate index matches the total number of plates# Run the model
M1_output <- Run_Model(stan_object = M1, stan_data = stan_data_M1)0.4 Plot outputs of Model 1
extract_qpcr_param(M1_output) %>% as.tibble()Warning: `as.tibble()` was deprecated in tibble 2.0.0.
ℹ Please use `as_tibble()` instead.
ℹ The signature and semantics have changed, see `?as_tibble`.# A tibble: 13 × 11
parameter mean se_mean sd `2.5%` `25%` `50%` `75%` `97.5%` n_eff Rhat
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 logit_phi 3.34 0.00916 0.859 1.76 2.73 3.31 3.90 5.16 8808. 1.00
2 beta_0[Plate_A] 37.9 0.00272 0.145 37.6 37.8 37.9 38.0 38.2 2828. 1.00
3 beta_0[Plate_B] 38.4 0.00267 0.141 38.1 38.3 38.4 38.5 38.7 2781. 1.00
4 beta_0[Plate_C] 38.4 0.00265 0.142 38.1 38.3 38.4 38.5 38.7 2850. 1.00
5 beta_0[Plate_D] 38.4 0.00282 0.150 38.1 38.3 38.4 38.5 38.7 2812. 1.00
6 beta_0[Plate_E] 38.1 0.00274 0.148 37.8 38.0 38.1 38.2 38.4 2914. 1.00
7 beta_0[Plate_F] 38.4 0.00270 0.142 38.1 38.3 38.4 38.5 38.7 2754. 1.00
8 beta_0[Plate_G] 38.1 0.00270 0.142 37.8 38.0 38.1 38.2 38.4 2743. 1.00
9 beta_0[Plate_H] 38.5 0.00265 0.140 38.2 38.4 38.5 38.6 38.7 2766. 1.00
10 beta_0[Plate_I] 39.2 0.00280 0.151 38.9 39.1 39.2 39.3 39.5 2882. 1.00
11 beta_1 -1.50 0.000211 0.00983 -1.52 -1.50 -1.50 -1.49 -1.48 2176. 1.00
12 gamma_0 0.600 0.00116 0.0854 0.435 0.543 0.600 0.657 0.773 5427. 1.00
13 gamma_1 -0.185 0.000146 0.0106 -0.206 -0.192 -0.185 -0.178 -0.164 5222. 1.00plot_qpcr_prob_det(M1_output)
plot_qpcr_cont_mod(M1_output)
plot_qpcr_curves(M1_output)
plot_qpcr_cont_mod_plate_specific(M1_output)
0.5 Run Model 2
M2 <- load_model('M2')# Prepare the data for going into the model
stan_data_M2 <- prep_stan_M2(
qpcr_data = qpcr,
sample_type = "Sample_type",
Ct = "Ct",
sample_name_column = "Sample_name",
standard_concentration = "Std_concentration",
plate_index = 'Plate')Plate index matches the total number of plates# Run the model
M2_output <- Run_Model(stan_object = M2, stan_data = stan_data_M2)0.6 Plot outputs of Model 2
extract_qpcr_param(M2_output) %>% as_tibble()# A tibble: 13 × 11
parameter mean se_mean sd `2.5%` `25%` `50%` `75%` `97.5%` n_eff Rhat
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 logit_phi 4.28 0.00528 0.691 3.03 3.79 4.24 4.73 5.74 17130. 1.00
2 beta_0[Plate_A] 39.4 0.00316 0.194 39.1 39.3 39.4 39.6 39.8 3759. 1.00
3 beta_0[Plate_B] 40.3 0.00395 0.221 39.8 40.1 40.3 40.4 40.7 3126. 1.00
4 beta_0[Plate_C] 40.4 0.00444 0.224 40.0 40.3 40.4 40.6 40.9 2543. 1.00
5 beta_0[Plate_D] 40.2 0.00385 0.230 39.8 40.1 40.2 40.4 40.7 3556. 1.00
6 beta_0[Plate_E] 39.9 0.00381 0.232 39.5 39.7 39.9 40.0 40.4 3710. 1.00
7 beta_0[Plate_F] 40.1 0.00377 0.217 39.7 40.0 40.1 40.3 40.6 3304. 1.00
8 beta_0[Plate_G] 39.9 0.00362 0.209 39.5 39.7 39.9 40.0 40.3 3335. 1.00
9 beta_0[Plate_H] 40.2 0.00360 0.200 39.8 40.1 40.2 40.4 40.6 3097. 1.00
10 beta_0[Plate_I] 40.6 0.00261 0.188 40.2 40.5 40.6 40.7 41.0 5199. 1.00
11 beta_1 -1.64 0.000308 0.0140 -1.67 -1.65 -1.64 -1.63 -1.61 2072. 1.00
12 gamma_0 0.838 0.000526 0.0457 0.749 0.807 0.837 0.868 0.929 7520. 1.00
13 gamma_1 -0.148 0.000190 0.0121 -0.170 -0.156 -0.148 -0.140 -0.124 4039. 1.00extract_est_conc(M2_output) %>% as_tibble()# A tibble: 172 × 5
sample_index Sample_name C_est_log `C_est_log_2.5%CI` `C_est_log_97.5%CI`
<dbl> <chr> <dbl> <dbl> <dbl>
1 1 2019629_10 -1.36 -2.83 -0.148
2 2 2019629_11 -2.84 -4.96 -1.16
3 3 2019629_12 -1.48 -3.48 0.0494
4 4 2019629_13 -3.18 -7.24 -0.466
5 5 2019629_14 -1.57 -3.62 -0.137
6 6 2019629_15 -3.41 -7.45 -0.623
7 7 2019629_16 -3.37 -7.33 -0.694
8 8 2019629_19 -3.21 -7.24 -0.449
9 9 2019629_2 -3.39 -7.30 -0.730
10 10 2019629_20 -1.11 -3.11 0.326
# ℹ 162 more rowsplot_qpcr_curves(M2_output)
plot_qpcr_prob_det(M2_output)
plot_qpcr_cont_mod(M2_output)
plot_qpcr_cont_mod_plate_specific(M2_output)
plot_est_conc(M2_output)
0.7 Run Model 3
M3 <- load_model('M3')# Trim metabarcoding data only for mock samples
moc_dat <- metabarcoding %>% select(Species,sp_idx,ini_conc,Mock_1:Mock_6)
# # Prepare the data for going into the model
stan_data_M3 <- prep_stan_M3(
metabarcoding_data = moc_dat,
mock_sequencing_columns = c('Mock_1','Mock_2','Mock_3','Mock_4','Mock_5','Mock_6'),
mock_initial_concentration = 'ini_conc',
species_index = 'sp_idx',
species_names = 'Species',
number_of_PCR = 43,
alpha_magnitude = 0.1)
# Run the model
M3_output <- Run_Model(stan_object = M3, stan_data = stan_data_M3)0.8 Plot outputs of Model 3
extract_amp_efficiecy(M3_output) Species sp_idx alpha alpha_2.5%_CI alpha_97.5%_CI
1 Brosme brosme 1 -0.014625116 -0.014733605 -0.014514664
2 Cyclopterus lumpus 2 -0.022590809 -0.022690726 -0.022492084
3 Hippoglossoides platessoides 3 -0.002313675 -0.002406314 -0.002220955
4 Leptoclinus maculatus 4 0.030800663 0.030722643 0.030878798
5 Mallotus villosus 5 -0.017323539 -0.017420855 -0.017226027
6 Maurolicus muelleri 6 0.000791902 0.000703401 0.000880933
7 Myoxocephalus scorpius 7 -0.013584736 -0.013681397 -0.013485525
8 Pholis gunnellus 8 -0.002699979 -0.002804276 -0.002594642
9 Pleuronectes platessa 9 0.002551719 0.002438675 0.002665334
10 Zz_Gadus morhua 10 0.000000000 0.000000000 0.000000000amp_eff_output_extract(M3_output) Species Pre-PCR Post-PCR ALR Post-PCR_est Post-PCR_est_2.5%_CI Post-PCR_est_97.5%_CI
1 Brosme brosme 0.08923200 0.05556938 0.01337365 0.05556998 0.05550922 0.05563432
2 Cyclopterus lumpus 0.17871590 0.07901771 0.70793133 0.07901803 0.07896072 0.07906964
3 Hippoglossoides platessoides 0.10093796 0.10672923 0.13663999 0.10672991 0.10668589 0.10677205
4 Leptoclinus maculatus 0.05519582 0.24240363 -0.46697893 0.24240237 0.24245477 0.24234604
5 Mallotus villosus 0.14545023 0.08065732 0.50196793 0.08065697 0.08060749 0.08070544
6 Maurolicus muelleri 0.10501282 0.12690236 0.17621634 0.12690231 0.12687255 0.12693228
7 Myoxocephalus scorpius 0.13199579 0.08596141 0.40490397 0.08596238 0.08591207 0.08602033
8 Pholis gunnellus 0.06633870 0.06898988 -0.28309260 0.06898974 0.06892673 0.06905443
9 Pleuronectes platessa 0.03907419 0.05093104 -0.81240387 0.05093088 0.05086523 0.05099679
10 Zz_Gadus morhua 0.08804659 0.10283804 0.00000000 0.10283744 0.10320533 0.10246868plot_amp_eff(M3_output)
0.9 Run Model 4
M4 <- load_model('M4')# Get column names for mock samples and environmental samples
mock_columns <- metabarcoding %>% select(Mock_1:Mock_6) %>% names()
sample_columns <- metabarcoding %>% select(-all_of(mock_columns),-Species,-sp_idx,-ini_conc) %>% names()
# Prepare the data for going into the model
stan_data_M4 <- prep_stan_M4(
metabarcoding_data = metabarcoding,
mock_sequencing_columns = mock_columns,
sample_sequencing_columns = sample_columns,
mock_initial_concentration = 'ini_conc',
species_index = 'sp_idx',
species_names = 'Species',
number_of_PCR = 43,
alpha_magnitude = 0.1)Warning: Using an external vector in selections was deprecated in tidyselect 1.1.0.
ℹ Please use `all_of()` or `any_of()` instead.
# Was:
data %>% select(mock_columns)
# Now:
data %>% select(all_of(mock_columns))
See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.M4_output <- Run_Model(stan_object = M4, stan_data = stan_data_M4)0.10 Plot outputs of Model 4
extract_amp_efficiecy(M4_output) Species sp_idx alpha alpha_2.5%_CI alpha_97.5%_CI
1 Brosme brosme 1 -0.014636236 -0.014746329 -0.014526717
2 Cyclopterus lumpus 2 -0.022600232 -0.022697729 -0.022502651
3 Hippoglossoides platessoides 3 -0.002322462 -0.002413868 -0.002229572
4 Leptoclinus maculatus 4 0.030791428 0.030714807 0.030869613
5 Mallotus villosus 5 -0.017331857 -0.017430582 -0.017235128
6 Maurolicus muelleri 6 0.000781859 0.000694592 0.000869834
7 Myoxocephalus scorpius 7 -0.013595752 -0.013692038 -0.013497046
8 Pholis gunnellus 8 -0.002710150 -0.002810974 -0.002607564
9 Pleuronectes platessa 9 0.002539945 0.002426005 0.002652835
10 Zz_Gadus morhua 10 0.000000000 0.000000000 0.000000000amp_eff_output_extract(M4_output) Species Pre-PCR Post-PCR ALR Post-PCR_est Post-PCR_est_2.5%_CI Post-PCR_est_97.5%_CI
1 Brosme brosme 0.08923200 0.05556938 0.01337365 0.05556427 0.05549767 0.05562778
2 Cyclopterus lumpus 0.17871590 0.07901771 0.70793133 0.07901568 0.07896372 0.07906538
3 Hippoglossoides platessoides 0.10093796 0.10672923 0.13663999 0.10672966 0.10668742 0.10677526
4 Leptoclinus maculatus 0.05519582 0.24240363 -0.46697893 0.24239713 0.24245530 0.24234740
5 Mallotus villosus 0.14545023 0.08065732 0.50196793 0.08065841 0.08060112 0.08070619
6 Maurolicus muelleri 0.10501282 0.12690236 0.17621634 0.12689516 0.12686752 0.12692255
7 Myoxocephalus scorpius 0.13199579 0.08596141 0.40490397 0.08595394 0.08590190 0.08601217
8 Pholis gunnellus 0.06633870 0.06898988 -0.28309260 0.06898547 0.06893025 0.06904372
9 Pleuronectes platessa 0.03907419 0.05093104 -0.81240387 0.05092422 0.05085477 0.05098981
10 Zz_Gadus morhua 0.08804659 0.10283804 0.00000000 0.10287606 0.10324033 0.10250974plot_amp_eff(M4_output)
extract_ini_prop(M4_output) Species 2019629_11 2019629_12 2019629_13 2019629_14 2019629_15 2019629_16 2019629_19 2019629_20 2019629_21 2019629_22 2019629_23 2019629_24 2019629_27 2019629_28 2019629_29 2019629_3 2019629_30 2019629_31 2019629_32 2019629_4 2019629_5 2019629_6 2019629_7 2019629_8 2020620_03 2020620_04 2020620_05 2020620_06 2020620_07 2020620_08 2020620_11 2020620_12 2020620_13 2020620_14 2020620_15 2020620_16 2020620_19 2020620_20 2020620_21 2020620_22 2020620_23 2020620_24 2020620_27 2020620_28 2020620_29 2020620_30 2020620_31 2020620_32 2021624_10 2021624_11 2021624_14 2021624_15 2021624_16 2021624_17 2021624_18 2021624_19 2021624_20 2021624_21 2021624_22 2021624_25 2021624_26 2021624_27 2021624_28 2021624_29 2021624_3 2021624_30 2021624_31 2021624_32 2021624_33 2021624_36 2021624_37 2021624_38 2021624_39 2021624_4 2021624_40 2021624_41 2021624_42 2021624_43 2021624_44 2021624_5 2021624_6 2021624_7 2021624_8 2021624_9
1 Brosme brosme 1.415181e-06 0.002082807 3.354987e-06 1.722911e-05 5.870391e-06 1.012995e-04 4.181448e-07 2.716857e-05 0.0009913585 1.201932e-05 4.772163e-04 7.176500e-04 1.397429e-05 3.878419e-05 8.022435e-06 5.584266e-05 9.261267e-07 5.964312e-04 1.037490e-05 2.497038e-06 6.589371e-04 2.899170e-06 1.701206e-04 4.519926e-05 4.844275e-05 6.440038e-02 7.293451e-05 7.972978e-05 4.789398e-06 1.714813e-05 1.082841e-04 1.030446e-04 3.546591e-06 4.246136e-05 9.310850e-07 6.082775e-07 6.498463e-05 1.569620e-05 1.094438e-05 3.995123e-05 9.097125e-06 5.520593e-06 9.959917e-06 3.624803e-06 4.521391e-07 3.855710e-05 4.491281e-06 2.615398e-06 8.969618e-06 9.191355e-06 1.277533e-04 3.187385e-04 2.447734e-05 3.797159e-04 1.325978e-05 0.0010056630 7.129744e-05 1.832772e-05 1.144469e-05 8.853224e-06 6.101692e-07 5.380331e-06 5.262214e-06 2.404518e-05 5.287450e-06 2.735549e-05 8.218425e-07 8.435091e-06 3.741725e-07 2.497735e-05 5.558586e-06 3.745630e-06 2.923228e-06 1.875514e-05 1.047599e-05 9.927437e-06 4.977193e-05 9.170290e-07 7.014595e-06 1.027505e-04 7.359990e-06 9.655292e-06 1.790810e-04 4.961625e-05
2 Cyclopterus lumpus 2.934829e-05 0.002554993 5.618473e-04 1.477091e-04 7.337894e-06 1.276433e-04 5.942565e-05 4.875297e-03 0.0011245171 2.774760e-04 1.159105e-03 4.874771e-04 1.443113e-04 5.210411e-05 6.899143e-05 7.425011e-04 8.298255e-01 4.892397e-05 1.392793e-05 4.304643e-05 2.909494e-05 3.940427e-06 6.472583e-06 1.858140e-02 1.382136e-04 9.491284e-05 9.844370e-05 1.123907e-04 1.632073e-04 2.212619e-05 1.393854e-04 1.016417e-05 4.131273e-03 4.618832e-06 6.928824e-04 8.025917e-07 6.607020e-06 2.055435e-05 1.419779e-05 1.158013e-04 1.220894e-05 7.197778e-06 1.301992e-05 4.868362e-06 1.328136e-04 1.109266e-04 5.955521e-06 3.336630e-06 1.649075e-04 4.183448e-04 2.888184e-06 2.581416e-05 3.303331e-05 1.732547e-04 1.803155e-05 0.0011941114 7.359509e-06 3.763236e-04 1.450399e-05 7.708388e-05 2.286324e-05 5.169193e-07 3.804637e-05 1.111535e-06 2.038243e-04 8.566381e-05 3.203477e-05 9.129178e-05 3.896347e-05 3.506217e-05 9.549339e-04 1.537720e-04 1.881901e-01 2.391901e-05 1.996741e-04 1.321172e-05 1.322030e-02 1.163289e-06 8.728257e-06 1.414476e-04 9.477359e-06 2.039613e-04 1.071704e-03 6.825352e-05
3 Hippoglossoides platessoides 5.471582e-02 0.057293427 9.969579e-01 7.167622e-01 4.152654e-06 6.663487e-05 9.995505e-01 9.768916e-01 0.5492569937 4.427771e-01 5.608376e-01 4.349454e-04 5.279678e-01 3.594403e-04 5.374506e-04 3.689006e-01 5.585051e-02 2.370209e-05 8.091940e-05 8.400991e-05 3.331042e-03 1.387532e-01 6.611328e-05 5.634454e-03 2.649512e-01 4.442640e-01 4.660690e-05 1.419282e-01 1.791165e-01 6.851022e-01 3.519341e-01 4.780484e-06 1.727635e-03 2.975826e-01 1.360731e-04 7.002988e-01 5.051775e-01 1.000186e-05 9.048779e-01 2.205254e-01 1.450003e-04 2.638441e-04 5.312622e-01 5.677549e-01 3.814985e-01 3.320617e-01 4.732425e-01 9.989186e-01 1.012633e-03 2.682975e-04 1.233816e-01 1.317242e-05 1.532839e-05 3.199779e-01 5.287629e-01 0.1838467831 3.110979e-01 6.628980e-04 9.958787e-01 6.682815e-01 8.967426e-01 1.945352e-01 7.741332e-01 8.672281e-01 5.746473e-01 8.382884e-01 8.422521e-01 6.982819e-01 6.689616e-01 6.566944e-01 1.538453e-01 7.884085e-01 4.899993e-01 3.358077e-01 1.949877e-01 7.845989e-01 4.931837e-01 9.994417e-01 8.266333e-01 7.096404e-05 4.913478e-02 7.030263e-02 3.195866e-01 2.080083e-01
4 Leptoclinus maculatus 2.561727e-04 0.014736649 1.019490e-04 5.531634e-02 1.424098e-06 1.962793e-05 5.253904e-05 6.956660e-04 0.4408383964 1.051972e-01 2.161861e-03 1.065053e-04 1.576098e-05 7.244948e-06 1.422991e-05 8.506843e-03 2.060788e-02 7.154529e-06 1.983154e-06 1.222681e-02 5.225718e-04 1.280393e-02 8.699997e-07 1.331597e-05 1.435772e-05 4.346079e-03 1.440141e-05 1.968071e-02 3.169288e-03 3.286582e-06 2.311718e-05 1.460566e-06 1.140317e-06 6.065106e-07 1.517619e-05 2.315445e-07 9.441791e-07 2.954956e-06 2.169066e-06 7.725814e-04 1.682809e-06 1.016375e-06 1.955753e-06 6.941421e-07 1.435372e-07 8.862682e-03 2.496878e-02 7.097842e-07 1.715311e-05 2.158113e-05 3.684917e-06 3.680282e-06 4.598755e-06 1.737278e-06 2.516880e-06 0.0002406133 1.038431e-06 3.971608e-05 2.559619e-06 8.786231e-04 1.166817e-07 7.280193e-08 2.178478e-03 1.737734e-06 1.098501e-02 8.632688e-08 5.543482e-05 3.164908e-04 9.844407e-08 4.298509e-03 1.796318e-01 1.623566e-05 4.202977e-03 3.548034e-06 6.307121e-03 1.872184e-06 8.649084e-04 2.554118e-07 1.341379e-06 2.037410e-05 2.200004e-03 3.775668e-02 2.609603e-05 7.653276e-07
5 Mallotus villosus 8.930124e-01 0.789849927 1.854221e-03 2.585052e-04 8.925349e-01 6.838727e-03 2.249050e-04 1.461067e-02 0.0010514682 4.634544e-04 8.457371e-04 3.228417e-02 2.345876e-04 3.632299e-03 3.348029e-04 3.285312e-01 2.235849e-02 3.996763e-05 7.864222e-04 7.311908e-01 9.903660e-01 2.654228e-02 2.146348e-01 9.721411e-01 6.926646e-03 8.281909e-02 3.018335e-03 1.217028e-02 5.245423e-06 1.907806e-05 4.021461e-01 3.565808e-01 2.672109e-01 3.979796e-01 7.791059e-01 2.505962e-04 3.015091e-02 4.885761e-04 5.020841e-04 6.290303e-01 3.181921e-01 8.192785e-01 1.744231e-01 2.489440e-01 2.577988e-01 4.793635e-01 2.385051e-01 2.678270e-04 2.386528e-01 4.213983e-01 3.896282e-01 2.968384e-01 1.102917e-01 2.809655e-04 2.221048e-04 0.6321884152 1.697831e-01 2.237696e-03 1.550121e-03 2.529663e-01 4.925789e-02 7.844417e-01 1.230560e-01 9.144333e-02 5.021865e-04 2.990552e-02 1.035389e-01 2.410187e-01 3.309114e-01 1.014023e-01 2.919260e-01 4.054886e-04 5.899977e-02 1.967401e-03 3.269578e-04 9.432559e-04 1.197697e-01 4.729366e-04 3.814325e-04 4.720429e-03 4.362248e-01 4.516925e-01 8.178032e-03 9.482103e-02
6 Maurolicus muelleri 8.014116e-07 0.001319192 2.003214e-06 9.051811e-06 3.478257e-06 5.960766e-05 1.034064e-04 1.835514e-05 0.0007786089 6.844829e-06 1.036662e-04 2.449416e-05 8.010932e-06 3.175918e-04 4.606976e-06 1.466981e-05 5.321405e-07 2.072512e-05 6.017047e-06 1.334901e-06 1.346827e-03 1.693626e-06 2.909350e-05 1.222864e-03 2.532930e-05 2.916053e-06 4.048982e-05 3.567179e-06 2.693041e-06 9.589495e-06 6.531641e-05 4.608588e-06 2.303271e-06 1.859510e-06 6.055614e-07 4.623944e-07 2.949528e-06 8.775238e-06 6.381756e-06 1.603762e-06 5.084631e-06 3.152417e-06 5.991483e-06 2.103309e-06 3.142992e-07 2.032079e-05 2.651092e-06 1.678584e-06 6.127346e-05 5.248709e-06 1.240626e-06 1.113865e-05 1.461520e-05 5.164053e-06 7.397710e-06 0.0006293748 3.196547e-06 1.112376e-05 6.812779e-06 3.864883e-07 3.532918e-07 2.237141e-07 2.754406e-06 6.091092e-06 3.070356e-06 2.762971e-07 4.608791e-07 1.994171e-07 2.387825e-07 1.135740e-06 3.255776e-06 2.226030e-06 1.633262e-06 1.431042e-04 5.921952e-06 5.749796e-06 8.425346e-06 6.160213e-07 3.942205e-06 5.953968e-05 4.015345e-06 1.548909e-04 6.241240e-06 2.391123e-06
7 Myoxocephalus scorpius 1.385461e-06 0.002036567 9.731625e-05 3.236733e-05 5.605788e-06 9.309622e-05 4.137236e-07 2.545402e-05 0.0009927215 1.906741e-04 1.247907e-04 4.210180e-05 1.323501e-05 3.780033e-05 4.632660e-05 1.651870e-04 1.789045e-05 3.460662e-05 1.009302e-05 2.919984e-05 2.306486e-05 2.857422e-06 4.472092e-06 4.396921e-05 1.423407e-04 1.322784e-04 7.026354e-05 6.243718e-06 5.474903e-05 1.641506e-03 1.036412e-04 9.816434e-05 7.568931e-04 3.329500e-06 9.683824e-05 6.420256e-07 6.198324e-05 1.510103e-05 1.032203e-05 7.780842e-05 9.058533e-06 5.475495e-06 1.661620e-04 3.507863e-06 4.264207e-07 2.583697e-06 6.226501e-05 2.307224e-04 1.122799e-04 8.830690e-06 4.804379e-05 1.888130e-05 3.497732e-04 8.939346e-06 1.289458e-05 0.0008777284 6.866543e-05 1.850670e-05 9.998431e-06 1.710380e-05 7.591789e-06 3.711926e-07 5.065088e-06 3.481004e-05 6.797093e-05 3.685159e-05 2.170604e-05 2.044722e-05 3.634602e-07 1.879777e-06 1.169350e-04 3.648709e-06 7.564891e-05 2.642140e-04 1.388748e-04 9.062039e-06 1.436680e-04 9.317437e-07 6.361893e-06 9.659958e-05 6.991942e-06 9.687853e-06 1.720623e-04 4.101096e-06
8 Pholis gunnellus 6.753464e-04 0.001557003 2.290855e-06 1.039515e-05 1.065488e-01 6.547493e-05 3.492443e-07 1.834224e-05 0.0008015670 1.917862e-01 5.794411e-06 2.818215e-05 8.926089e-06 3.669095e-04 3.008257e-05 2.103843e-04 1.129560e-05 1.626346e-01 6.905742e-06 9.342936e-06 1.676998e-05 1.023224e-01 2.985483e-06 3.181101e-05 3.738318e-02 6.645211e-02 1.616383e-03 8.392439e-02 9.981054e-02 1.214140e-01 7.467609e-05 5.140845e-06 7.260870e-01 5.214841e-05 2.198874e-01 2.994380e-01 3.284473e-06 1.013748e-05 2.693932e-04 7.146597e-03 5.659702e-06 3.390843e-06 1.377572e-01 2.436785e-06 3.605564e-01 1.794855e-02 4.259676e-02 3.299076e-04 3.055194e-02 3.290385e-01 1.076977e-04 3.020731e-01 1.634170e-05 6.692784e-02 8.485252e-06 0.0398311805 3.524280e-06 1.640276e-04 7.509954e-06 3.316049e-03 3.496458e-05 1.014147e-05 5.054616e-03 2.166586e-03 5.463781e-02 2.643090e-05 4.936939e-03 3.273914e-03 3.763700e-05 8.585230e-03 3.475949e-01 2.046727e-01 5.676571e-02 1.196046e-05 3.358095e-02 6.345747e-06 1.351411e-02 6.637338e-07 4.314352e-06 1.223345e-03 2.623425e-02 6.713754e-02 4.516880e-01 2.912351e-02
9 Pleuronectes platessa 7.716346e-07 0.001341990 1.872854e-06 1.357892e-06 3.537187e-06 5.459441e-05 2.917021e-07 1.653275e-05 0.0007823947 6.660535e-06 4.822851e-06 2.328875e-05 7.432724e-06 2.074939e-05 4.244094e-06 2.305838e-06 5.183849e-07 2.073698e-05 5.585933e-06 1.314857e-06 1.325676e-05 1.551575e-06 2.479369e-06 2.862359e-05 2.240727e-06 2.776881e-06 4.039352e-05 3.413197e-06 2.515043e-06 9.105410e-06 6.314497e-05 4.190409e-06 2.348740e-06 1.744917e-06 5.878669e-07 4.545638e-07 2.624621e-06 8.345022e-06 5.666822e-06 1.485094e-06 4.679261e-06 2.979055e-06 5.389564e-06 2.001199e-06 3.002040e-07 1.498740e-06 2.418015e-06 1.720324e-06 4.664429e-06 5.291688e-06 1.156412e-06 1.071233e-05 1.294277e-05 4.876760e-06 7.580816e-06 0.0005832363 2.929167e-06 1.020728e-05 6.436845e-06 3.669386e-07 3.258735e-07 2.102328e-07 2.487429e-07 4.373014e-07 2.879414e-06 2.555319e-07 4.390073e-07 1.893805e-07 2.278839e-07 1.020154e-06 2.982411e-06 2.090042e-06 1.544995e-06 9.934591e-06 5.644822e-06 5.098163e-06 7.879666e-07 6.080877e-07 3.662453e-06 5.610253e-05 3.853557e-06 5.207214e-06 5.717687e-06 2.234373e-06
10 Zz_Gadus morhua 5.130650e-02 0.127227444 4.172723e-04 2.274449e-01 8.849356e-04 9.925733e-01 7.782947e-06 2.820931e-03 0.0033819741 2.592823e-01 4.342794e-01 9.658512e-01 4.715860e-01 9.951671e-01 9.989512e-01 2.928704e-01 7.132649e-02 8.365731e-01 9.990778e-01 2.564116e-01 3.692462e-03 7.195653e-01 7.850826e-01 2.257303e-03 6.903680e-01 3.374855e-01 9.949817e-01 7.420911e-01 7.176705e-01 1.917620e-01 2.453423e-01 6.431877e-01 7.697066e-05 3.043310e-01 6.358994e-05 9.450813e-06 4.645282e-01 9.994199e-01 9.430092e-02 1.422885e-01 6.816154e-01 1.804289e-01 1.563550e-01 1.832818e-01 1.175447e-05 1.615897e-01 2.206091e-01 2.428973e-04 7.294134e-01 2.488264e-01 4.866978e-01 4.006864e-01 8.892372e-01 6.122396e-01 4.709448e-01 0.1396028940 5.189611e-01 9.964612e-01 2.511925e-03 7.445364e-02 5.393265e-02 2.100616e-02 9.552630e-02 3.909375e-02 3.589446e-01 1.316291e-01 4.916123e-02 5.698838e-02 4.909395e-05 2.289555e-01 2.591834e-02 6.331574e-03 2.017603e-01 6.617494e-01 7.644366e-01 2.144066e-01 3.592447e-01 8.016596e-05 1.729499e-01 9.935084e-01 4.861744e-01 3.727272e-01 2.190865e-01 6.679198e-01bar_plot_est_ini_prop(M4_output)
heatmap_plot_est_ini_prop(M4_output)
0.11 Run Model 5
M5 <- load_model('M5')mock_columns <- metabarcoding %>% select(Mock_1:Mock_6) %>% names()
sample_columns <- metabarcoding %>% select(-all_of(mock_columns),-Species,-sp_idx,-ini_conc) %>% names()
qpcr <- qpcr %>% filter(qpcr$Sample_name%in%sample_columns|qpcr$Sample_type=='STANDARD')
stan_data_M5 <- prep_stan_M5(
qpcr_data = qpcr,
sample_type = "Sample_type",
Ct = "Ct",
sample_name_column = "Sample_name",
standard_concentration = "Std_concentration",
plate_index = 'Plate',
metabarcoding_data = metabarcoding,
mock_sequencing_columns = mock_columns,
sample_sequencing_columns = sample_columns,
mock_initial_concentration = 'ini_conc',
species_index = 'sp_idx',
species_names = 'Species',
number_of_PCR = 43,
alpha_magnitude = 0.1)
M5_output <- Run_Model(stan_object = M5, stan_data = stan_data_M5,
treedepth = 12,iterations = 2000,warmup = 1000)0.12 Plot outputs of Model 5
extract_amp_efficiecy(M5_output) Species sp_idx alpha alpha_2.5%_CI alpha_97.5%_CI
1 Brosme brosme 1 -0.014633216 -0.014744261 -0.014525211
2 Cyclopterus lumpus 2 -0.022599699 -0.022701110 -0.022501947
3 Hippoglossoides platessoides 3 -0.002320010 -0.002412516 -0.002229666
4 Leptoclinus maculatus 4 0.030792999 0.030713767 0.030872151
5 Mallotus villosus 5 -0.017330826 -0.017427473 -0.017232206
6 Maurolicus muelleri 6 0.000783399 0.000698113 0.000869815
7 Myoxocephalus scorpius 7 -0.013591807 -0.013688780 -0.013495259
8 Pholis gunnellus 8 -0.002707492 -0.002808783 -0.002607558
9 Pleuronectes platessa 9 0.002540987 0.002428899 0.002657853
10 Zz_Gadus morhua 10 0.000000000 0.000000000 0.000000000amp_eff_output_extract(M5_output) Species Pre-PCR Post-PCR ALR Post-PCR_est Post-PCR_est_2.5%_CI Post-PCR_est_97.5%_CI
1 Brosme brosme 0.08923200 0.05556938 0.01337365 0.05556741 0.05550019 0.05562806
2 Cyclopterus lumpus 0.17871590 0.07901771 0.70793133 0.07901169 0.07894880 0.07906306
3 Hippoglossoides platessoides 0.10093796 0.10672923 0.13663999 0.10673308 0.10668896 0.10676845
4 Leptoclinus maculatus 0.05519582 0.24240363 -0.46697893 0.24239572 0.24243387 0.24235939
5 Mallotus villosus 0.14545023 0.08065732 0.50196793 0.08065606 0.08060837 0.08071151
6 Maurolicus muelleri 0.10501282 0.12690236 0.17621634 0.12689425 0.12688119 0.12691487
7 Myoxocephalus scorpius 0.13199579 0.08596141 0.40490397 0.08596221 0.08591018 0.08601365
8 Pholis gunnellus 0.06633870 0.06898988 -0.28309260 0.06898829 0.06893373 0.06903962
9 Pleuronectes platessa 0.03907419 0.05093104 -0.81240387 0.05092277 0.05085888 0.05099777
10 Zz_Gadus morhua 0.08804659 0.10283804 0.00000000 0.10286851 0.10323582 0.10250362plot_amp_eff(M5_output)
extract_ini_prop(M5_output) Species 2019629_11 2019629_12 2019629_13 2019629_14 2019629_15 2019629_16 2019629_19 2019629_20 2019629_21 2019629_22 2019629_23 2019629_24 2019629_27 2019629_28 2019629_29 2019629_3 2019629_30 2019629_31 2019629_32 2019629_4 2019629_5 2019629_6 2019629_7 2019629_8 2020620_03 2020620_04 2020620_05 2020620_06 2020620_07 2020620_08 2020620_11 2020620_12 2020620_13 2020620_14 2020620_15 2020620_16 2020620_19 2020620_20 2020620_21 2020620_22 2020620_23 2020620_24 2020620_27 2020620_28 2020620_29 2020620_30 2020620_31 2020620_32 2021624_10 2021624_11 2021624_14 2021624_15 2021624_16 2021624_17 2021624_18 2021624_19 2021624_20 2021624_21 2021624_22 2021624_25 2021624_26 2021624_27 2021624_28 2021624_29 2021624_3 2021624_30 2021624_31 2021624_32 2021624_33 2021624_36 2021624_37 2021624_38 2021624_39 2021624_4 2021624_40 2021624_41 2021624_42 2021624_43 2021624_44 2021624_5 2021624_6 2021624_7 2021624_8 2021624_9
1 Brosme brosme 1.084275e-06 0.0011853257 2.638443e-06 1.948868e-05 4.490163e-06 0.0005719925 5.653550e-07 1.331362e-05 0.0009170173 9.466096e-06 7.886411e-04 0.0057228407 1.449947e-05 2.372685e-04 7.866191e-05 7.182526e-05 5.389256e-07 2.723692e-03 3.778322e-04 2.251081e-06 6.278555e-04 6.030906e-06 6.379148e-04 3.189110e-05 1.395437e-04 9.382238e-02 0.0005591680 2.543656e-04 8.129761e-06 1.197901e-05 6.767489e-05 2.328119e-04 4.053948e-06 5.514905e-05 1.359511e-06 8.460932e-07 1.112598e-04 2.108672e-04 7.826098e-06 4.253886e-05 1.458523e-05 4.012742e-06 6.409536e-06 2.886199e-06 7.459251e-07 4.224235e-05 3.357848e-06 1.430504e-06 1.824905e-05 7.254730e-06 2.377986e-04 4.795344e-04 8.364123e-05 9.141864e-04 1.567708e-05 0.0007306597 1.316946e-04 0.0002151497 7.025773e-06 8.815820e-06 4.001648e-07 5.041292e-06 5.328829e-06 2.437309e-05 4.047115e-06 3.134331e-05 4.440765e-07 8.591089e-06 3.614645e-07 2.952519e-05 4.173675e-06 2.452731e-06 2.011953e-06 2.619229e-05 2.324418e-05 7.197522e-06 7.420387e-05 4.743427e-07 5.283513e-06 0.0006018506 7.233017e-06 8.220886e-06 2.091707e-04 1.324306e-04
2 Cyclopterus lumpus 2.940836e-05 0.0013797732 5.627168e-04 1.837527e-04 5.446614e-06 0.0007510910 6.183485e-05 4.730986e-03 0.0009572994 3.452867e-04 1.939501e-03 0.0036232953 2.206277e-04 2.994153e-04 1.028545e-03 1.012253e-03 8.894563e-01 1.271701e-04 4.544335e-04 5.318625e-05 2.731213e-05 7.486510e-06 1.631897e-05 1.855168e-02 4.078276e-04 1.289774e-04 0.0007144508 3.568020e-04 5.309320e-04 1.695845e-05 8.960796e-05 1.601244e-05 4.074964e-03 3.726418e-06 6.982586e-04 1.021440e-06 6.271086e-06 2.789879e-04 9.092122e-06 1.294030e-04 2.171438e-05 5.242005e-06 8.375139e-06 3.801492e-06 1.380797e-04 1.276886e-04 4.238567e-06 2.108439e-06 4.837327e-04 5.300197e-04 3.028731e-06 2.126018e-05 1.113419e-04 3.919553e-04 2.029369e-05 0.0009648881 6.467663e-06 0.0067323782 8.835633e-06 8.144021e-05 2.337007e-05 2.245276e-07 4.140288e-05 6.612972e-07 3.011722e-04 9.795229e-05 3.229780e-05 9.617275e-05 3.818829e-05 4.165355e-05 9.560079e-04 1.464110e-04 2.332548e-01 3.449158e-05 6.047031e-04 8.772711e-06 2.015036e-02 7.366947e-07 6.678623e-06 0.0007304096 9.636789e-06 2.879432e-04 1.292002e-03 1.846840e-04
3 Hippoglossoides platessoides 5.720291e-02 0.0598270661 9.970853e-01 9.023942e-01 3.098622e-06 0.0003724158 9.995391e-01 9.793076e-01 0.5500232977 5.801000e-01 9.435589e-01 0.0034071969 9.525346e-01 3.116461e-03 8.778903e-03 5.065309e-01 5.985378e-02 6.234920e-05 5.586353e-03 1.071136e-04 3.342946e-03 4.591563e-01 2.477108e-04 5.667137e-03 8.113364e-01 6.469808e-01 0.0003265289 4.868983e-01 6.089970e-01 8.292580e-01 4.550078e-01 8.134446e-06 1.733250e-03 4.216644e-01 1.385657e-04 7.003619e-01 9.161168e-01 1.335546e-04 9.848814e-01 2.519795e-01 3.704847e-04 3.112710e-04 6.211964e-01 6.782534e-01 3.815083e-01 3.878611e-01 5.967505e-01 9.991221e-01 3.121752e-03 3.439444e-04 2.335047e-01 1.225074e-05 5.430755e-05 7.905537e-01 9.212505e-01 0.2035593565 6.390756e-01 0.0124756951 9.976490e-01 7.211476e-01 9.452585e-01 1.986290e-01 8.542355e-01 8.999535e-01 8.875757e-01 9.630208e-01 8.846839e-01 7.384898e-01 6.689275e-01 8.460105e-01 1.560904e-01 7.925886e-01 6.073997e-01 9.364510e-01 6.220963e-01 9.853281e-01 7.517685e-01 9.995112e-01 9.774641e-01 0.0003665476 9.071056e-02 1.094602e-01 3.882767e-01 6.061632e-01
4 Leptoclinus maculatus 2.672724e-04 0.0154789297 1.012020e-04 6.963406e-02 1.206164e-06 0.0001193845 5.283095e-05 6.891567e-04 0.4405203645 1.379051e-01 3.634730e-03 0.0008585200 2.449461e-05 4.845599e-05 2.254862e-04 1.168338e-02 2.208802e-02 2.181966e-05 7.261193e-05 1.579370e-02 5.190000e-04 4.238180e-02 2.177812e-06 8.941922e-06 4.220635e-05 6.323777e-03 0.0001166321 6.749973e-02 1.077740e-02 2.720474e-06 1.676533e-05 2.451906e-06 1.229578e-06 5.098519e-07 1.545327e-05 2.797592e-07 1.034822e-06 4.557249e-05 1.507463e-06 8.815143e-04 3.222137e-06 8.624113e-07 1.465855e-06 5.475722e-07 2.040119e-07 1.035544e-02 3.149706e-02 4.736253e-07 5.050013e-05 2.629868e-05 6.494017e-06 4.002042e-06 1.689975e-05 2.358382e-06 2.871987e-06 0.0001938783 1.038868e-06 0.0007102065 1.978941e-06 9.484220e-04 7.944192e-08 3.789045e-08 2.403808e-03 1.708450e-06 1.695824e-02 6.084238e-08 5.808999e-05 3.344261e-04 9.812398e-08 5.538150e-03 1.821505e-01 1.555788e-05 5.209448e-03 5.602307e-06 2.011612e-02 1.451337e-06 1.317038e-03 1.563879e-07 1.150037e-06 0.0001265067 4.053489e-03 5.874782e-02 3.127246e-05 1.244009e-06
5 Mallotus villosus 9.334850e-01 0.8892390691 1.857490e-03 3.246065e-04 8.930378e-01 0.0630672037 2.244447e-04 1.463815e-02 0.0010152950 5.860506e-04 1.413556e-03 0.2724748127 3.902209e-04 3.394486e-02 5.429593e-03 4.511707e-01 2.396850e-02 1.083011e-04 5.958892e-02 9.445348e-01 9.919356e-01 8.786033e-02 8.197481e-01 9.737712e-01 2.123354e-02 1.205555e-01 0.0386973239 4.172642e-02 9.096415e-06 1.293137e-05 5.191052e-01 8.564719e-01 2.672425e-01 5.638897e-01 7.790638e-01 2.502306e-04 5.470111e-02 1.132471e-02 5.394169e-04 7.187357e-01 8.412042e-01 9.777885e-01 2.039694e-01 2.973816e-01 2.578386e-01 5.600080e-01 3.007704e-01 2.613858e-04 7.402716e-01 5.484626e-01 7.375912e-01 4.722668e-01 6.096723e-01 6.685145e-04 3.720320e-04 0.6948533358 3.488858e-01 0.0421117119 1.535311e-03 2.729864e-01 5.194616e-02 8.010134e-01 1.358079e-01 9.491928e-02 7.574460e-04 3.435542e-02 1.087656e-01 2.548965e-01 3.309481e-01 1.306550e-01 2.960614e-01 4.000798e-04 7.315911e-02 5.442149e-03 1.019899e-03 1.181072e-03 1.825300e-01 4.690475e-04 4.433119e-04 0.0417466301 8.048678e-01 7.033943e-01 9.900156e-03 2.762439e-01
6 Maurolicus muelleri 5.944828e-07 0.0008517984 1.801875e-06 1.011161e-05 2.490704e-06 0.0003397235 1.043887e-04 9.412707e-06 0.0007430413 5.670363e-06 1.651721e-04 0.0001357022 8.229510e-06 2.914405e-03 5.123376e-05 1.836762e-05 3.481959e-07 5.760111e-05 2.123722e-04 1.272472e-06 1.335523e-03 3.049583e-06 1.061731e-04 1.107795e-03 7.389808e-05 2.765206e-06 0.0003053051 7.772169e-06 4.713325e-06 7.151639e-06 4.692892e-05 7.157795e-06 2.546151e-06 1.417686e-06 8.943470e-07 5.551955e-07 3.014613e-06 1.278333e-04 4.314688e-06 1.203573e-06 9.966698e-06 2.549011e-06 3.744575e-06 1.776026e-06 5.046980e-07 2.256147e-05 1.882394e-06 1.060853e-06 1.771722e-04 4.033409e-06 1.360100e-06 1.072630e-05 4.923193e-05 7.269380e-06 8.932240e-06 0.0004322735 2.872513e-06 0.0001257419 4.910469e-06 2.347822e-07 2.521485e-07 1.063627e-07 2.828702e-06 6.063128e-06 2.139652e-06 1.678562e-07 2.495891e-07 1.287045e-07 2.615520e-07 8.271633e-07 2.618867e-06 1.497260e-06 1.201017e-06 3.791213e-04 1.281306e-05 3.974226e-06 1.210253e-05 3.727619e-07 3.047806e-06 0.0003422961 4.687876e-06 2.364451e-04 5.727749e-06 3.602554e-06
7 Myoxocephalus scorpius 1.037059e-06 0.0011104326 9.180411e-05 3.925498e-05 3.733945e-06 0.0005455078 5.123545e-07 1.545983e-05 0.0009157543 2.338765e-04 2.008255e-04 0.0002150459 1.369629e-05 2.255208e-04 6.856527e-04 2.238983e-04 1.835227e-05 9.902784e-05 3.396647e-04 3.554104e-05 1.792345e-05 5.399060e-06 1.028145e-05 2.809385e-05 4.251287e-04 1.910545e-04 0.0005512401 1.306632e-05 1.706298e-04 1.962032e-03 6.691753e-05 2.228462e-04 7.420499e-04 2.383148e-06 1.003434e-04 9.062682e-07 1.057316e-04 2.112003e-04 7.263894e-06 8.758803e-05 1.376795e-05 4.170984e-06 1.823812e-04 2.752783e-06 6.924819e-07 2.239238e-06 7.486544e-05 2.233169e-04 3.266720e-04 6.402897e-06 8.670112e-05 1.778802e-05 1.860649e-03 1.123676e-05 1.362187e-05 0.0006362791 1.299044e-04 0.0002122764 6.841726e-06 1.763137e-05 7.466093e-06 1.623537e-07 5.154285e-06 3.574028e-05 9.545584e-05 4.170909e-05 2.216874e-05 2.131607e-05 3.414342e-07 1.246049e-06 1.184942e-04 2.233809e-06 9.099409e-05 6.755288e-04 4.165934e-04 6.532554e-06 2.172648e-04 4.785340e-07 4.778395e-06 0.0005729187 8.261587e-06 8.204730e-06 1.996778e-04 5.822814e-06
8 Pholis gunnellus 7.045685e-04 0.0008836846 2.094043e-06 1.194421e-05 1.065704e-01 0.0004087377 4.015623e-07 1.022312e-05 0.0008108107 2.513707e-01 5.945560e-06 0.0001548605 9.832014e-06 3.328202e-03 4.362950e-04 2.866142e-04 1.150740e-05 7.970165e-01 2.379052e-04 1.100956e-05 1.385099e-05 3.385946e-01 7.381518e-06 2.179411e-05 1.144132e-01 9.674589e-02 0.0209761447 2.877249e-01 3.394819e-01 1.469422e-01 4.942238e-05 7.842245e-06 7.261017e-01 7.147446e-05 2.198297e-01 2.993661e-01 3.408961e-06 1.314945e-04 2.881339e-04 8.180225e-03 1.065080e-05 2.924455e-06 1.611244e-01 1.998509e-06 3.604735e-01 2.093912e-02 5.369627e-02 3.247291e-04 9.473574e-02 4.282585e-01 1.997147e-04 4.805514e-01 5.617079e-05 1.653998e-01 1.035602e-05 0.0431864353 3.162615e-06 0.0029063570 5.058288e-06 3.579866e-03 3.608698e-05 1.012937e-05 5.577271e-03 2.248655e-03 8.441528e-02 3.009891e-05 5.183608e-03 3.462086e-03 3.786751e-05 1.105492e-02 3.524323e-01 2.057803e-01 7.032855e-02 1.719295e-05 1.070531e-01 4.417046e-06 2.058840e-02 3.888708e-07 3.662400e-06 0.0104769011 4.840665e-02 1.044692e-01 5.487410e-01 8.482760e-02
9 Pleuronectes platessa 6.253574e-07 0.0008293071 1.806947e-06 1.276602e-06 2.312187e-06 0.0003218891 3.767001e-07 9.075610e-06 0.0007663634 5.137660e-06 4.737064e-06 0.0001324275 7.440166e-06 1.249961e-04 4.466423e-05 2.066949e-06 3.795547e-07 5.695299e-05 2.010456e-04 1.222875e-06 1.187378e-05 3.034434e-06 6.568793e-06 1.857294e-05 3.688313e-06 2.353523e-06 0.0003260123 7.175554e-06 4.339109e-06 7.131110e-06 4.366298e-05 6.981177e-06 2.350272e-06 1.445183e-06 8.423174e-07 6.370193e-07 2.899658e-06 1.183957e-04 4.430048e-06 1.114510e-06 8.207952e-06 2.107970e-06 3.823429e-06 1.630509e-06 4.790609e-07 1.250947e-06 1.976908e-06 1.039100e-06 1.042127e-05 3.817690e-06 1.324872e-06 9.790286e-06 4.362919e-05 6.574700e-06 8.310009e-06 0.0004794231 3.017291e-06 0.0001179571 4.173084e-06 2.056430e-07 2.138207e-07 8.886514e-08 1.379425e-07 2.929241e-07 2.261538e-06 1.540324e-07 2.420578e-07 1.213613e-07 2.146242e-07 7.515525e-07 2.703474e-06 1.336128e-06 1.191476e-06 1.444285e-05 1.324625e-05 3.912535e-06 7.365152e-07 3.343125e-07 2.807942e-06 0.0003281194 4.065641e-06 4.423459e-06 5.006962e-06 3.515683e-06
10 Zz_Gadus morhua 8.307531e-03 0.0292146135 2.931487e-04 2.738134e-02 3.690413e-04 0.9335020544 1.552678e-05 5.766161e-04 0.0033307564 2.943875e-02 4.828803e-02 0.7132752983 4.677635e-02 9.557604e-01 9.832410e-01 2.900000e-02 4.602296e-03 1.997266e-01 9.329289e-01 3.945985e-02 2.168081e-03 7.198189e-02 1.792174e-01 7.929127e-04 5.192465e-02 3.524646e-02 0.9374271941 1.155115e-01 4.001580e-02 2.177890e-02 2.550602e-02 1.430238e-01 9.536830e-05 1.430980e-02 1.507332e-04 1.749263e-05 2.894850e-02 9.874174e-01 1.425662e-02 1.996125e-02 1.583432e-01 2.187834e-02 1.350360e-02 2.434954e-02 3.891325e-05 2.064040e-02 1.719948e-02 6.238510e-05 1.608042e-01 2.235715e-02 2.836771e-02 4.662641e-02 3.880518e-01 4.204436e-02 7.829744e-02 0.0549634707 1.176043e-02 0.9343925261 7.768894e-04 1.229369e-03 2.727469e-03 3.418486e-04 1.920676e-03 2.809678e-03 9.888287e-03 2.422323e-03 1.253496e-03 2.690859e-03 4.699977e-05 6.667341e-03 1.218131e-02 1.061500e-03 1.055297e-02 5.695431e-02 2.486440e-01 1.345460e-02 2.334137e-02 1.679758e-05 2.206521e-02 0.9447078201 5.192764e-02 2.338327e-02 5.133930e-02 3.243400e-02bar_plot_est_ini_prop(M5_output)
bar_plot_est_ini_prop(M4_output)
heatmap_plot_est_ini_prop(M5_output)
plot_est_ini_conc(M5_output)